高维数字混沌系统的理论设计与FPGA实现
Theoretical Design and FPGA-Based Implementation of Higher-Dimensional Digital Chaotic Systems
摘要：
传统上，混沌系统是建立在数学上的无限精度域。然而，量化是任何数字设备不可避免的，这会导致动态退化。为了解决这一问题，人们提出了许多方法，如扰动混沌状态和级联多个混沌系统。本文旨在发展一种新的方法来设计有限精度域中的高维数字混沌系统（HDDCS）。该系统基于随机序列控制的混沌产生策略。证明了它满足Devaney混沌定义。此外，我们还计算了HDDCS的李雅普诺夫指数。通过FPGA平台演示了HDDCS在图像加密中的应用。由于HDDCS的每个操作都以相同的固定精度执行，因此不会发生量化损失。因此，它提供了一个完美的解决方案的动力学退化的数字混沌。
英文摘要：
Traditionally, chaotic systems are built on the domain of infinite precision in mathematics. However, the quantization is inevitable for any digital devices, which causes dynamical degradation. To cope with this problem, many methods were proposed, such as perturbing chaotic states and cascading multiple chaotic systems. This paper aims at developing a novel methodology to design the higher-dimensional digital chaotic systems (HDDCS) in the domain of finite precision. The proposed system is based on the chaos generation strategy controlled by random sequences. It is proven to satisfy the Devaney's definition of chaos. Also, we calculate the Lyapunov exponents for HDDCS. The application of HDDCS in image encryption is demonstrated via FPGA platform. As each operation of HDDCS is executed in the same fixed precision, no quantization loss occurs. Therefore, it provides a perfect solution to the dynamical degradation of digital chaos.
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